6 Trade Discounts, Cash - Pearson

6 C h a p t e r

Trade Discounts, Cash

Discounts, Markup, and

Markdown

L e a r n i n g O b j e ct i v e s

Upon completing this chapter, you will be able to do the following: Solve problems involving trade discounts. Calculate equivalent single rates of discount for a discount

series. Apply methods of cash discount. Solve problems involving markup based on either cost or

selling price. Solve problems involving markdown. Solve integrated problems involving discounts, markup, and

markdown.

??

When you mark up your products to include Expenses and Profits, what is the Selling

price?

Selling price

Profit Expenses Cost

In a business, traditional accounting profit is calculated by subtracting costs and expenses from sales revenue for a specified period. Determining a suitable selling price for each product or service is crucial for long-term sustainability. Some firms use a cost plus methodology, marking up the cost of each product or service by a certain percentage that is large enough to cover expenses and still leave a respectable profit. Other organizations select their desired profit percentages first, and then work backwards to set their prices.

Suppose you were operating a bicycle shop and selling adult mountain bikes that cost $200 each from your supplier. Using a cost plus approach you might add a 20% markup to the cost of bikes sold in the shop in order to cover your additional expenses and make a profit. In this case, you would charge your customers $240 for the bikes, and your resulting profit percentage would be $40/$240 = 1623%. If, however, you wanted to price the bikes in order to earn 20% profit, you would have to charge your customers $250 for the same bicycles ($50/$250 5 20%).

202 c h a p t e r 6 T r ad e D iscou n t s , C as h D iscou n t s , M a r k u p, a n d M a r k do w n

Introduction

Th supply chain defi es the channels or stages that a product passes through as it is converted from a raw material to a fin shed product purchased by the consumer. Figure 6.1 outlines this process.

A Supply Chain

Manufacturer

Distributor

Wholesaler

Retailer

Consumer

By the time the product is purchased by the consumer, the raw materials have been converted by the manufacturer, distributed through the wholesaler, and offered for sale by the retailer. In some supply chains, the distributor and wholesaler are separated. In other supply chains, the manufacturer also serves as the wholesaler. Within the supply chain, all of the channels must make a profit on the product to remain in business.

Each channel applies a markup above its cost to buy the merchandise, which increases the price of the product. Sometimes a manufacturer or supplier sets a list price and then offers a trade discount or a series of trade discounts from that price to sell more product or to promote the product within the supply chain. Also, any of the channels within the supply chain may offer a cash discount to encourage prompt payment for the product. When the product is sold to the consumer, the regular selling price may be marked down or discounted to a sale price in response to competitors' prices or other economic conditions.

Price, cost, and expenses of a product determine the profit for that product. Understanding the relationships between these variables is crucial in maintaining a successful business. In this chapter, we will learn how to calculate the cost of products if trade discounts are offered within the supply chain, as well as how to calculate the amount of cash to be paid when cash discounts are offered for early payment. We will also learn how to calculate price and profit when the cost is marked up, as well as the discounted price and resulting profit or loss when a product is offered "on sale."

Figure 6.1 Terminology Used in the Supply Chain

Manufacturer's costs

markup

List price

Trade discount(s)

Net price to wholesaler

Cost to wholesaler

markup

List price

Trade discount(s)

Net price to retailer

Cost to retailer

markup

markdown Regular

Sale

selling

price

price

or

discounted

price

Net price to consumer

Selling price

Profit Expenses Cost

If a list price is set and trade discounts are offered, what is the cost?

6 . 1 D e t e r mi n i n g C os t w i t h T r ad e D iscou n t s 203

6.1 Determining Cost with Trade Discounts

puting discount amounts, discount rate, net price, and list price

The supply chain is made up of manufacturers, distributors, wholesalers, and retailers. Merchandise is usually bought and sold among the members of the chain on credit terms. The prices quoted to other members often involve trade discounts. A trade discount is a reduction of a list price or manufacturer's suggested retail price (MSRP) and is usually stated as a percent of the list price or MSRP.

Trade discounts are used by manufacturers, distributors, and wholesalers as pricing tools for several reasons, such as to

(a) determine different prices for different levels of the supply chain;

(b) communicate changes in prices;

(c) enable changes in prices.

When computing a trade discount, keep in mind that the rate of discount is based on the list price.

AMOUNT = RATE OF ? LIST

OF DISCOUNT DISCOUNT PRICE

A = d ? L or A = dL

Formula 6.1

When the amount of the discount and the discount rate are known, the list price can be determined. Rearrange Formula 6.1 to determine the list price.

LIST PRICE = AMOUNT OF DISCOUNT

RATE OF DISCOUNT

L

=

A d

Since the rate of trade discount is based on the list price, computing a rate of discount involves comparing the amount of discount to the list price. Rearrange Formula 6.1 to determine the rate of trade discount.

RATE OF DISCOUNT = AMOUNT OF DISCOUNT

LIST PRICE

d

=

A L

Po i n t e r s a n d P i tf a ll s

This diagram is a useful aid in remembering the various forms of the amount of discount formula A 5 dL. Variables on the same line are multiplied together. Variables on different lines are divided.

A

d

L

For example, in solving for d, note that A is above the L. Therefore, d 5A/L. Similarly, L 5 A/d.

204 c h a p t e r 6 T r ad e D iscou n t s , C as h D iscou n t s , M a r k u p, a n d M a r k do w n

Th net price is the remainder when the amount of discount is subtracted from the list price. The net price is the price to the supplier, and becomes the cost to the purchaser.

NET PRICE = LIST PRICE - AMOUNT OF DISCOUNT

N=L-A

Formula 6.2

To compute the amount of the discount and the net price when the list price and discount rate are known, fi st apply Formula 6.1 to determine the amount of the trade discount, and then apply Formula 6.2 to calculate the net price.

Example 6.1A

An item listed at $80.00 is subject to a trade discount of 25%. Compute

(i) the amount of discount;

(ii) the net price.

Solution (i) Amount of trade discount 5 Rate of discount 3 List price 5 (0.25)(80.00) 5 $20.00

(ii) Net price 5 List price 2 Trade discount 5 80.00 2 20.00 5 $60.00

Example 6.1B

The 30% discount on a tennis racket amounts to $89.70. Compute

(i) the list price;

(ii) the net price.

Solut i o n

(i)

List

price

=

Amount of discount Rate of discount

=

89.70 0.3

=

$299.00

(ii) Net price 5 List price 2 Amount of discount 5 299.00 2 89.70 5 $209.30

Example 6.1C

Find the rate of discount for (i) snowboards listed at $280.00 less a discount of $67.20; (ii) snow-sport helmets listed at $129.99 whose net price is $84.49; (iii) goalie pads whose net price is $368.99 after a discount of $81.00.

Solut i o n

(i)

Rate

of

discount

=

Amount of discount List Price

=

67.20 280.00

=

0.24

=

24.00%

(ii) Since Net price 5 List price 2 Amount of discount (Formula 6.2),

Amount of discount 5 List price 2 Net price 5 129.99 2 84.49 5 $45.50

Rate

of

discount

=

Amount of discount List price

=

45.50 129.99

=

0.350027

=

35.00%

6 . 1 D e t e r mi n i n g C os t w i t h T r ad e D iscou n t s 205

(iii) Since Net price 5 List price 2 Amount of discount (Formula 6.2),

List price 5 Net price 1 Amount of discount 5 368.99 1 81.00 5 $449.99

Rate

of

discount

=

Amount of discount List price

=

81.00 449.99

=

0.180004

=

18.00%

B. The net price factor approach

Instead of computing the amount of discount and then deducting this amount from the list price, the net price can be found by using the more effici t net factor approach developed in the following illustration.

Referring back to Example 6.1A, the solution can be restated as follows:

List price Less trade discount 25% of 80.00 Net price

$80.00 20.00 $60.00

Example 6.1D

Since the discount is given as a percent of the list price, the three dollar values may be stated as percents of list price:

List price Less trade discount Net price

$80.00

20.00

$60.00

100% of list price 25% of list price 75% of list price

Note: The resulting "75%" is called the net price factor or net factor (in abbreviated form NPF) and is obtained by deducting the 25% discount from 100%.

NET PRICE = 100% - % DISCOUNT

FACTOR (NPF)

The resulting relationship between net price and list price may be stated generally.

NET PRICE = LIST PRICE ? NET PRICE

FACTOR (NPF)

These relationships can be restated in algebraic terms:

Convert the % discount into its decimal equivalent represented by d, and express 100% by its decimal equivalent, 1.

NET PRICE FACTOR = 1 - d

Let the list price be represented by L, and let the net price be represented by N.

N = L(1 - d) ???????????????????????????? Formula 6.3

Another way to derive the net price formula is to substitute Formula 6.1 into Formula 6.2 and then collect the similar terms. If we substitute Amount of discount, A 5 dL, into N 5 L 2 A, we obtain N 5 L 2 dL. Since L is a common factor, we can rewrite the formula as N 5 L(1 2 d).

Find the net price for

(i) list price $36.00 less 15%; (ii) list price $86.85 less 3313%.

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